Many patients, particularly those from ethnic minorities, are unable to access the therapeutic benefit of allogeneic hematopoietic cell transplantation due to the lack of a suitable donor. For such patients, umbilical cord blood can offer an alternative source of hematopoietic cells. However, adults typically require the concurrent use of two cord blood units (DCBT) at considerable expense. In adults such transplants are also associated with delayed immune reconstitution, increased rate of infections and a higher treatment related mortality than transplants from conventional donors. Recently the use of haploidentical (partially matched related donor) hematopoietic cell transplants (haplo-HCT) using T-cell-replete marrow grafts and post- transplant cyclophosphamide (PTCy), have been shown to produce high rates of engraftment and low treatment related mortality (TRM) when used with a non-myeloablative preparative regimen, in patients who lack conventional donors. However, such transplants have limited efficacy in aggressive/advanced myeloid malignancies because of a high relapse rate. In an institutional pilot trial, we have assessed the use of T- replete mobilized peripheral blood (PBSC) and a myeloablative preparative regimen with haplo-HCT + PTCy. Despite the advanced and high-risk nature of the malignancies treated, estimated 6 month TRM was 14% and disease-free survival was 72%. All patients engrafted and developed full donor chimerism in CD3+ and CD33+ cells by day +30. A multi-institutional phase II trial is therefore proposed within the BMT CTN to confirm these encouraging results. The proposed trial will test the hypothesis that this novel approach to myeloablative haplo-HCT is safe and effective when used in a multi-institutional setting. Upon successful completion of this phase II trial, a randomized phase 111 comparison is proposed between this approach to haplo-HCT and myeloablative DCBT. The objective of this phase 111 study will be to directly compare these two approaches to alternative donor transplantation with respect to safety, toxicity, efficacy, cost and immune reconstitution. This trial would definitively determine the best option for myeloablative transplantation in patients with advanced malionancies who lack a matched-sibling or matched unrelated donor RELEVANCE (See instructions): The proposed research addresses a significant current deficiency in public health. Specifically, it tests a novel strategy that will enable curative myeloablative blood stem cell transplants in patients (particularly those from underserved minorities) who are currently unable to access them due to lack of a conventional donor. If successful, it will transform the standard-of-care by offering life-saving therapy to patients who would have died from their cancer and close a major disparity in healthcare access for ethnic minorities.